Question

The ratio of two angles of a triangle is 2 : 7. If the third angle equals the sum of these two angles, the measure of largest angle is: (a) 20° (b) 50° (c) 70° (d) 90° of Vimal​

Answer 1

Answer:

90° is the answer

Explanation:

A/Q

Angle sum property of triangle.

2 X + 7 x + 2 X + 7 x= 180°

4x + 14x = 180°

18x = 180°

x=180°/18

x=10°

So, First angle= 2 × 10° = 20°

Second angle = 7 × 10° = 70°

Third angle = 20° + 70° = 90°

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Answer 2

Given: The ratio of two angles of a triangle is 2:7

To find The measure of the largest angle

Solution: Let the ratio of the given two angles of a triangle be 2x and 7x, then the 1st angle= 2x and the 2nd angle = 7x

∴ The 3rd angle = 2x+7x [∵ it is the  3rd angle equals the sum of the 1st angle and the 2nd angle]

We know that the summation of all angles of a triangle is equal to 180°.

∴ 2x+7x+(2x+7x)=180°

⇒18x=180°  [adding the like terms]

⇒ x=180/18

⇒x=10

The 1st angle is (2×10) that is 20°

The 2nd angle is (7×10) that is 70°

The 3rd angle is {(2×10)+(7×10)}={20+70}=90°

∴ The largest angle = the 3rd angle = 90°

Hence the measure of the largest angle is (d) 90°.